NETWORK ANALYSIS & SYNTHESIS

UTTARAKHAND TECH. UNIVERSITY

UTU

B TECH (SEM III),2011-2012

SUB:-NETWORK ANALYSIS & SYNTHESIS  

time : 3hr] 

Total marks :100

SECTION A

Q1:- Attempt any four of the following :

1. (i) What is cutset matrix? How is it prepared?
   (ii) Derive general equilibrium equation of a network using cutset matrix Q, branch admittance [Y_b], current source vector [I_s] and voltage source vector [V_s].
   
2. Write the matrix loop equation for the network shown in figure.1 using the loop analysis.
   
   

   

   fig.1

3. Draw the oriented graph of the network for the fundamental cut-set matrix given below:

   

   
   

   
   
4. Explain the term Duality and draw the dual of network as shown in figure 1.
5. Define the terms (A) Node (B) Branch (C) Tree& Cotree (D) Cutset (E) Tieset.
6. Derive the relation between Branch voltage matrix, Twig voltage matrix and Node voltage matrix of a network as shown in figure 2.

   

   fig.2
   

   
   

SECTION B

Q2:- Attempt any four of the following :

1. Derive maximum power transfer theorem for a DC as well as for an AC network.
2. State and prove the Millman's theorem as applicable to current sources.
3. Use superposition theorem to determine the voltage v and power dissipated by the 3 ohmresistor of the following network Fig.3.

   

   fig.3

   
   
4. Find the Thevenin's equivalent of the circuit as shown in fig.4

   

   fig.4

   
   
5. Find the Norton's equivalent of the circuit shown in fig.3
6. State and prove reciprocity theorem with the help of a suitable example.

SECTION C

Q3:- Attempt any two of the following :

1. Describe all the necessary steps for the construction of Bode Magnitude and Phase plot, and draw and Bode plot for
    
   
   
2. (i) Calculate the range of K for which the system is given by characteristics equation is stable.6s⁴ – 5s³ – 3s² – s – k = 0.
   (ii) Check the stability criteria of the following polynomial by applying Routh-Hurwitz criterion:
   
   s⁵ - 3s⁴ – 6s³ – 5s² – 3s – 2 = 0
3. Determine the ABCD parameters of the following of the networks as shown in fig.5

   

   fig.5

   
   

SECTION D

Q4:- Attempt any two of the following :

1. Obtain the Z-parameter of the following in terms of all other parameter .
2. Obtain the Y-parameter of the network given below.

   

   fig.6

   
   
3. A 2-port network made up of passive linear resistor is fed at port 1 by an ideal voltage source of V volts. It is loaded at port 2 by a resistance R.
   (i) With V = 5volts and R = 3 ohm, the current at ports 1&2 were 0.44A and 0.2A respectively.
   (ii) With V = 10 volts and R = 5 ohm, the current at ports 2 was 0.15 A determine π equivalent circuit of 2-port network.

SECTION E

Q5:- Attempt any two of the following :

1. Find the R-C representation of Foster- I & II forms of the following function.
   
2. Check whether the function given below is a positive real function.
   
3. Find the first and second foster form of the driving point impedance function.
   

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GOOD LUCK!!!!